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Simplifying 5b2 + 5b + -18 = (3b + -2)(2b + 5) Reorder the terms: -18 + 5b + 5b2 = (3b + -2)(2b + 5) Reorder the terms: -18 + 5b + 5b2 = (-2 + 3b)(2b + 5) Reorder the terms: -18 + 5b + 5b2 = (-2 + 3b)(5 + 2b) Multiply (-2 + 3b) * (5 + 2b) -18 + 5b + 5b2 = (-2(5 + 2b) + 3b * (5 + 2b)) -18 + 5b + 5b2 = ((5 * -2 + 2b * -2) + 3b * (5 + 2b)) -18 + 5b + 5b2 = ((-10 + -4b) + 3b * (5 + 2b)) -18 + 5b + 5b2 = (-10 + -4b + (5 * 3b + 2b * 3b)) -18 + 5b + 5b2 = (-10 + -4b + (15b + 6b2)) Combine like terms: -4b + 15b = 11b -18 + 5b + 5b2 = (-10 + 11b + 6b2) Solving -18 + 5b + 5b2 = -10 + 11b + 6b2 Solving for variable 'b'. Reorder the terms: -18 + 10 + 5b + -11b + 5b2 + -6b2 = -10 + 11b + 6b2 + 10 + -11b + -6b2 Combine like terms: -18 + 10 = -8 -8 + 5b + -11b + 5b2 + -6b2 = -10 + 11b + 6b2 + 10 + -11b + -6b2 Combine like terms: 5b + -11b = -6b -8 + -6b + 5b2 + -6b2 = -10 + 11b + 6b2 + 10 + -11b + -6b2 Combine like terms: 5b2 + -6b2 = -1b2 -8 + -6b + -1b2 = -10 + 11b + 6b2 + 10 + -11b + -6b2 Reorder the terms: -8 + -6b + -1b2 = -10 + 10 + 11b + -11b + 6b2 + -6b2 Combine like terms: -10 + 10 = 0 -8 + -6b + -1b2 = 0 + 11b + -11b + 6b2 + -6b2 -8 + -6b + -1b2 = 11b + -11b + 6b2 + -6b2 Combine like terms: 11b + -11b = 0 -8 + -6b + -1b2 = 0 + 6b2 + -6b2 -8 + -6b + -1b2 = 6b2 + -6b2 Combine like terms: 6b2 + -6b2 = 0 -8 + -6b + -1b2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 6b + b2) = 0 Factor a trinomial. -1((4 + b)(2 + b)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + b)' equal to zero and attempt to solve: Simplifying 4 + b = 0 Solving 4 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + b = 0 + -4 b = 0 + -4 Combine like terms: 0 + -4 = -4 b = -4 Simplifying b = -4Subproblem 2
Set the factor '(2 + b)' equal to zero and attempt to solve: Simplifying 2 + b = 0 Solving 2 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + b = 0 + -2 b = 0 + -2 Combine like terms: 0 + -2 = -2 b = -2 Simplifying b = -2Solution
b = {-4, -2}
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